I'm glad this thread resurfaced, as it combines two things I love, giving my opinion and lists
Most influential is an interesting list to consider, as it will probably cover books I read all in my formative years (i.e. 20-30 something years ago). Here goes, in no particular order:
1)
Lord of the Rings - JRR Tolkein What can I say, it introduced me to grand fantasy and I read it at a time I was getting into RPG's. It brings back so many memories of playing AD&D and particularly Rolemaster (which I set in Middle Earth as GM). Yes, I was a college science geek and no mistake.
2)
The Mayor of Casterbridge - Thomas Hardy This was probably the first great novel I read outside of school and under my own volition. I fell for Hardy's work and have since read all his Wessex novels.
3)
To Your Scattered Bodies Go - Philip Jose Farmer This was not the first SF book I read (that was A Fall of Moondust by Clarke, which just misses the cut), but it was an early one and was hugely influential on me. I followed up reading all the Riverworld books and his World of Tiers series. This was in all in my teens, and surely shaped my appreciation of SF.
4)
The Human Factor - Graham Greene Not Greene's greatest work, not his most famous. I could easily have said The Quiet American, or The Heart of the Matter, or many others. I read 15 or so Greene novels in my late teens and early twenties. However, I picked The Human Factor because it's central theme (that you cannot discount the possibility that human connections and emotions may affect key decisions, against all logic) affected my thinking from the moment I set the book down.
5.
The Biochemical Basis of Neuropharmacology - Cooper, Bloom and Roth This textbook wasn't even on our reading list at university, but I started to attain an interest in neuroscience physiology and pharmacology and read this book cover to cover while waiting in the laundromat at college. Then I re-read it. Then I did my PhD in neuropharmacology. It was all because the book was pitched so well and I was an interested sponge at the time. I wouldn't necessarily recommend it to the lay reader.